Game Engine: Object with character physics shakes for some reason
The problem you are experiencing is due to the way blender calculates the collision for the quads on your ground plane. There are two ways to fix this, you can use a cube as ground instead (with collision bounds set to box), or you can set your plane's collision type to box, even though a plane is infinitely thin.

To help see the problem,
First turn on Physics Visualization.
This does not effect anything except what you see, so in the end it does not matter if it is on or off.


If your plane's collision bounds are not set to anything, blender automatically calculates it as if it were made up of two triangles.


However, if you set it to Box collision, This problem goes away.


If you use a thin cube instead for your ground, (with collision type set to box) this problem goes away entirely.


Another thing you can try is putting all of your logic bricks and python on a invisible low detail object, for a collision mesh, and having your detailed car as no-collision but parented to the collision mesh. Even if this alone does not remove the shaking, it will dramatically help performance.